Question

Find the average rate of change of the function from x 1 to x 2.
​f(x)equalsminus3x squaredminusx from x 1equals5 to x 2equals6
Question content area bottom
Part 1
A.minus one sixth
minusone sixth
B.
minus2
C.
minus34
D.one half
one half

Answer 1

To find the average rate of change of the function \( f(x) = -3x^2 - x \) from \( x_1 = 5 \) to \( x_2 = 6 \), we will use the formula for the average rate of change:

\[
\text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
\]

1. Calculate \( f(5) \):

\[
f(5) = -3(5)^2 - 5 = -3(25) - 5 = -75 - 5 = -80
\]

2. Calculate \( f(6) \):

\[
f(6) = -3(6)^2 - 6 = -3(36) - 6 = -108 - 6 = -114
\]

3. Now, substitute \( f(5) \) and \( f(6) \) into the average rate of change formula:

\[
\text{Average Rate of Change} = \frac{f(6) - f(5)}{6 - 5} = \frac{-114 - (-80)}{1} = \frac{-114 + 80}{1} = \frac{-34}{1} = -34
\]

Therefore, the average rate of change of the function from \( x_1 = 5 \) to \( x_2 = 6 \) is:

\[
\boxed{-34}
\]

The answer is \( C. -34 \).